Experimental Verification of Hematite Ingot Mould Heat - DSpace

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Experimental Verification of Hematite Ingot Mould Heat Capacity and its Direct Utilisation in Simulation of Casting Process Bedřich Smetana1, Monika Žaludová1, Markéta Tkadlečková2, Jana Dobrovská1,

Simona Zlá1, Karel Gryc2, Petr Klus2, Karel Michalek2, Pavel Machovčák3, Lenka

Řeháčková1

1VŠB-TU Ostrava, Faculty of Metallurgy and Materials Engineering, Department of Physical Chemistry and Theory of Technological Processes, Regional Materials Science and Technology Centre, 17. listopadu 2172/15, Ostrava-Poruba, Czech Republic 2VŠB-TU Ostrava, Faculty of Metallurgy and Materials Engineering, Department of Metallurgy and Foundry, Regional Materials Science and Technology Centre, 17. listopadu 2172/15, Ostrava-Poruba, Czech Republic 3 VÍTKOVICE HEAVY MACHINERY a.s. (VHM), Ruská 2887/101, Ostrava-Vítkovice, Czech Republic 00420 597 321 594

00420 597 323 396

[email protected]

XXXXXXX URL Article note

Heat capacity of alloys (metals) is one of the crucial thermo-physical parameters used for

process behaviour prediction in many applications. Heat capacity is an input variable for many

thermo-dynamical (e.g. Thermocalc, Pandat, MTData,...) and kinetic programs (e.g. IDS-

Solidification analysis package,...). The dependences of heat capacity on common variables

(temperature, pressure) are also commonly used as the input data in software packages (e.g.

ProCast, Magmasoft, ANSYS Fluent...) that are applicable in the field of applied research for

simulations of technological processes. It follows from the above that the heat capacities of

materials, in our case alloys, play a very important role in the field of basic and applied research.

Generally speaking, experimental data can be found in the literature, but corresponding (needed)

data for the given alloy can very seldomly be found or can differ from the tabulated ones. The

knowledge of proper values of heat capacities of alloys at the corresponding temperature can be

substantially used for addition to and thus towards the precision of the existing database and

simulation software. The paper presents the values of Cp measured for the hematite ingot mould

and comparison of the measured data with the Cp obtained using the software CompuTherm with

respect to simulation of technological casting process.

Journal of thermal analysis and calorimetry. 2013, vol. 112, issue 1, p. 473-480. http://dx.doi.org/10.1007/s10973-013-2964-z

DSpace VŠB-TUO http://hdl.handle.net/10084/96328 13/5/2013

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heat capacity, DTA, 3D DSC, phase transition temperatures, computation,

simulations, real process

Abbreviations

Introduction

Heat capacity [1] and other material properties (phase transition temperatures,

latent heats, surface tension, interface tension,...) [2–9] of alloys (metals) are

crucial thermo-physical quantities for many applications. Many of these data are

accessible in the literature, but it is very often difficult to find data for a given

material (with exact chemical composition), as well as for the required

temperature interval. The data found for given material in different literature

resources sometimes even differs [2, 3, 7].

Heat capacities are typically used as basic data in many calculating

software packages (SW), e.g. Thermocalc, MTData, PANDAT, IDS and others.

Proper thermo-physical and thermo-dynamic data are used (necessary for

simulations) also in SW, such as Magmasoft and ProCAST.

This paper deals with the investigation of heat capacity (Cp) of a hematite ingot

mould, Fig. 1, used in VÍTKOVICE HEAVY MACHINERY a.s. for casting of

steel ingots. This kind of mould is used for the production of heavy steel forging

ingots that are used for the production of many products in the assortment of

VÍTKOVICE HEAVY MACHINERY a.s. (steam generators, heat exchangers,

collectors for conventional and nuclear power engineering,...). Constantly

increasing demands on higher quality of products lead to the necessity of

optimization of technological processes. The best way to optimize the production

process is to have proper data from operation, proper material data and simulation

SW. In this paper the measured values of heat capacity Cp of a hematite mould are

compared with Cp values calculated using CompuTherm. Both experimental and



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calculated dependences of Cp were used for the simulation of process of casting of

a steel ingot with use of ProCAST SW, and the obtained results are discussed.

Theory

Heat capacity can be expressed as heat (Q) absorbed/released by the sample

(material) during its heating or cooling between the temperatures T1 and T2 [1]:

Mean value of Cp at constant pressure can be expressed by the equation (1):

12 TTQC−

= (1)

For comparison of the heat capacity of different materials it is necessary to relate

this quantity to the amount of material. If the Cp is related to the (sample) mass

then the so-called specific heat capacity at constant pressure is defined [1].

The fastest way to obtain the values of heat capacity is the utilization of

calculation relation(s) or calculation SW. Considering the multi-component alloys

(steels and other alloys) it is possible to use the Neumann-Kopp rule to calculate

Cp dependence on temperature [1].

Secondly, it is possible to use SW for calculation of Cp. JmatPro, IDS or

CompuTherm (ProCast sub module) are very often used for calculation of

temperature dependence of Cp. Although utilization of the calculation SW is very

comfortable and fast, this procedure is mostly based on theoretical assumptions,

limitations and approximations connected with the composition of the alloy,

temperature interval, calculation model limitations and others. Cp values are

mostly calculated only with respect to the chemical composition, but the Cp value

(dependence) may be influenced by structure, phases present in the sample and

influence of the deformational state. Therefore, the best way to obtain proper data

for the system under investigation is by carrying out an experiment.



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Almost all classical DSC devices make it possible to perform two basic methods

for heat capacity determination. The first is the continuous method and the second

is the so-called stepwise method. Special equipment is used for the so called

DROP method. General description of these three methods can be found

e.g. in [10].

Continuous method is the fastest method for Cp determination and was used for

experimental measurements in this work. The scheme of the continuous method is

shown in Figure 2.

The heat capacity determined on the basis of DSC experiment comprises three

main sequences: 1st sequence - adjusted isothermal dwell, 2nd sequence - linear

heating in the whole measured temperature interval and the 3rd sequence is

isothermal dwell at the temperature that makes it possible to cover the desired

temperature interval. All three sequences must be performed with empty crucibles

(B), with the sample (S) and with the reference sample (C). Consecutively, the

heat capacity can be calculated according to the following formula [10]:

)()(

BCS

BSCpCp AAm

AAmCC−×−×

×= (2)

where, AB, AS, AC in [mW] are segments corresponding to the heat effects detected

for the measurement of blank (empty crucibles), measurement with the sample

and the reference sample, CpC [J K-1 g-1] is the heat capacity of the reference

sample, Cp [J K-1 g-1] is the heat capacity of the measured sample, mS [mg] and mC

[mg] are masses of the sample and the reference sample.

Numerical simulation of real casting process

The principle of numerical simulation, as published in [11–17], is the numerical

solution of each task divided into the three stages: pre-processing, processing and

post-processing.



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Pre-processing includes the geometric modelling and the computational mesh

generation process, and definition of calculation. The whole 3D ingot mould

geometry was created in the CAD system SolidWorks. Comparison of the real and

CAD geometry of the casting system is shown in Figs. 1 A and B. The

computational mesh was generated in Visual-Mesh, which is a part of the packet

of ProCAST software. Figure 1C presents the final computational mesh of the

casting system. Figure 1 D shows the final 3D ingot geometry.

Determination of some boundary, operating and initial conditions is not usually

difficult. The quality of the results of the numerical simulation of the temperature

field, volume defects in ingots, especially macro-segregation of elements, is

mainly determined by the quality of the thermo-dynamic and thermo-physical

properties of steel and of ingot mould material. In the simulation section this

paper is focused on comparison of temperature fields in an ingot mould obtained

using the values of Cp calculated using CompuTherm (Computherm enables

calculation only of the enthalpy dependence on the temperature, not the specific

heat temperature dependence, not the separately specific heat temperature

dependence and latent heats of the running phase transitions. Therefore, the

dependence of enthalpy on temperature was recalculated to the heat capacity

dependence including the latent heat of the phase transition in the investigated

region. So, the so-called apparent heat capacity was obtained [18, 19]) with the

values of Cp (apparent Cp) obtained experimentally using the DSC measurements,

other conditions (parameters) during simulation were unchanged.



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Experimental

Samples characterisation

Samples of the ingot mould were supplied by VÍTKOVICE HEAVY

MACHINERY a.s. Samples were machined into the form of cylinders (5 mm in

diameter and 17 mm in height with a mass of ~2100 mg for DSC analysis and

3.5 mm in diameter and 3 mm height with mass of ~160 mg for TG/DTA

analysis), chemical composition is shown in Table 1 (supplied by VÍTKOVICE

HEAVY MACHINERY a.s., the analyses were performed with use of

spectroscopy with glow discharge and combustion analysers). Prior to the

performed TG/DTA and DSC analyses the samples were ground in order to

remove a possible oxidation layer, then cleaned in acetone by simultaneous

ultrasound impact.

Simultaneous TG/DTA analysis

Alloys containing carbon are predisposed to the decarburisation at higher

temperatures (due to the high carbon diffusivity) [20]. Therefore, simultaneous

thermal analysis (TG/DTA) was performed in order to check the possible

decarburisation (mass loss) of an ingot mould sample during the analysis. The

TG/DTA was performed in the temperature interval of 300–1700 K in an inert

atmosphere of Ar (6N). Analyses were performed for two heating rates,

10 and 20 K min-1. Simultaneous TG/DTA analyses were performed in corundum

crucibles.

TG and DTA curves obtained for different heating rates are presented in Figure 3.

According to the obtained DTA curves the running phase transitions were

checked and compared with the DSC results. The observed TG curve, in

dependence on temperature, showed whether the mass of sample was changed

during the experiment or not.



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TG/DTA analyses were performed until the complete melting of the sample.

During the heating rate of 10 K min-1 mass loss was observed, which

corresponded with high probability with the decarburisation degree of the sample.

The start of the carbon loss was observed at around 950 K. The constant trend in

the mass loss of carbon was observed up to the temperature of ~1300 K. Then the

mass loss was substantially faster than between the temperatures of 950–1300 K.

Over 1300 K the sample melting was observed and therefore also the faster

decarburisation, as observed from the TG curve(s). The sample mass loss was

1.9 %. Assuming that the sample mass loss is 1.9 wt %, then the carbon content

decrease is more than 50 %. On the basis of the preliminary TG/DTA analyses (at

10 K min-1) it was necessary to modify the conditions of thermal analyses

experiments in order to avoid possible decarburisation that might have

corresponding influence on the values of heat capacity. Another heating rate was

set to be 20 K min-1. The mass loss of the sample was not observed (Figure 3) at

such a fast heating rate in the temperature region from 300–1300 K. In the melting

region the decrease of mass was approx. 0.1 %. That means that the maximum

reduction of the carbon content was no more than 4 % (if complete melting of the

sample was realised).

With respect to the observed facts, the heating rate of 20 K min-1 was chosen as

suitable for the performed DSC analyses (blank, calibration with corundum,

analysed sample).

Moreover, the temperature calibration was performed with use of standard metals

(Sn, Al, Ag, purity 5N) at corresponding heating rates.



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DSC analysis

Heat capacity (apparent heat capacity, heat capacity including latent heat of the

phase transition) of the ingot mould was measured with use of the Setaram MHTC

96 Line (Multi High Temperature Calorimeter) equipped with 3D heat flux DSC

B-type measurement sensor making it possible to perform experiments up to

1823.15 K. Measurements were performed in the temperature interval between

500–1100 K in an inert atmosphere of He (6N, flow rate 20 ml min-1; helium is

more suitable for obtaining the Cp values using scanning methods because of a

substantially high thermal conductivity in comparison with Ar). The resulting

value of heat capacity dependence was obtained from three measurements. The

prepared cylinders of the samples were put into the corundum sleeve (shut by

corundum lid), the sleeve was inserted in to the Pt–crucible and shut by the Pt–lid,

and consequently the Pt crucible was inserted into the 3D DSC sensor and

covered by the corundum plate.

The temperature programme started from 300 K by linear heating (5 K min-1) of

the sample up to the temperature of 423.15 K. At this temperature the first

isothermal dwell was realised. Subsequently the linear heating (20 K min-1) to the

second isotherm (1373.15 K) followed. Experimental values of Cp were obtained

from the temperature interval of 500–1300 K (temperature interval without

disturbing effects caused by change of isotherms and heating mode, Figure 3).

The same temperature programme was set for calibration measurements with

corundum (purity 4N8) and for the blank.

Heat capacity measurements were checked with respect to the known heat

capacity of corundum. The relative standard deviation from three measurements

(computed from three runs performed with corundum) for the temperature interval

between 500–1300 K was ± 0.2 %. Comparison with the generally accepted Cp



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values of corundum was performed. The standard deviation (mean value)

calculated from experimentally obtained values and from the generally accepted

Cp for the specific temperature is 5 % (in the measured temperature interval).

The temperature calibration was performed also with use of standard metals (Sn,

Al, Ag, purity 5N) at the heating rate of 20 K min-1.

Results and discussion

Phase transitions

DTA and DSC analysis also revealed two thermal effects, see Figs. 3 and 4. The

first thermal effect corresponds with the change of magnetic properties

(ferromagnetic to paramagnetic, temperature of the Curie point was evaluated,

TC = 1019 K (DTA, 20 K min-1). The second heat effect (DTA, 20 K min-1) can

be, with high probability, attributed to the transition α + Cgrafitic → γ [6] (α –

ferrite, Cgrafitic-graphitic carbon, γ-austenite). This transition takes place between

the temperatures of 1071–1108 K. Identical thermal effects were observed during

the DSC analysis, TC = 1036 K and α + Cgrafitic → γ takes place between 1079–

1131 K. Transition temperatures obtained using DSC are shifted to the higher

temperatures, whereas the main reason for this phenomenon is the amount of the

sample used for the DSC analysis. The bigger the mass, the longer the time

needed for heat transfer (the transitions must not take place in each part of the

sample at the same time) within the whole volume of the sample. The shift of

temperatures might have been caused also by the detection limit of the sensor. In

the case of large samples and at relatively high heating rates, the beginning and

termination of the heat effect followed by the phase transition can be very often

more unclear in comparison with the experiments with small samples and lower

heating rates (this fact might have also influenced the results).



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Enthalpy and consequently the apparent heat capacity Cp of the hematite ingot

mould was calculated using the CompuTherm SW, Fig. 4. When using this SW

only one phase transition can be observed (1007-1067 K), which is in contrast

with the real DSC and DTA experiments, when two transitions were observed.

Probably, the authors of CompuTherm SW suppose, that the peak (heat effect)

includes both the magnetic transition and transition of α + Cgrafitic → γ in close

proximity (heat effects could overleap over each other). The authors of this SW do

not present the models used for thermo-physical and thermo-dynamic quantity

calculations in their instruction manuals and thus it is not clear which algorithm

the authors used for the Cp calculation. So in fact it is not clear, whether the

received Cp (enthalpy respectively) is just calculated, calculated and corrected

with respect to the experiment or whether it is only experimental. Probably the

calculation model with its limitations and simplifications may give somewhat

different results in comparison with the experiments.

Heat capacity

Experimentally obtained and calculated values of apparent heat capacity are

presented in Table 2 and graphically shown in Figure 4.

The experimentally obtained Cp values (on the basis of three measurements) are

very close to the values calculated with use of the Computherm SW in the

temperature interval of 500–1000 K, and in the interval of 1175–1300 K. The

differences between experimental and calculated values are also presented in

Table 2. The Cp dependence trends are the same. The experimentally obtained

dependence shows mild curvature in the observed intervals. Heat capacity values

significantly differ between the temperatures of 1000–1175 K due to running

phase transition(s). The differences could probably be attributed to the

simplifications and limitations that are implemented in the calculation models.



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The calculating relations and models are also often derived on the basis of

experimental data (that are at present insufficient) and theoretical assumptions,

which are valid most often for a certain interval of chemical composition. The

data obtained by extrapolation beyond this interval (e.g. concentration interval)

can be less relevant.

Comparison of simulation results using calculated and experimental Cp values

Simulations were performed with use of the ProCAST SW. Comparison of the

calculated results with the experimental and theoretical results are presented in

Figure 5. A very important parameter was observed: the temperature field in the

hematite ingot mould, which defines, together with the heat flux, also the heat

transfer coefficients and ambient temperature, and also the character of the

solidification, as well as the size of the volume defects, such as shrinkage or

porosity. Figure 5 presents the temperature fields of real mould acquired with

thermo-vision measurements compared with the results obtained with calculated

and experimental Cp dependences after one hour, 2 hours and 3 hours and 20

minutes after the casting process. The temperature fields (real, calculated by the

CompuTherm Cp and experimental Cp) are identical for the observed times: 1 hour

and 3 hours and 20 minutes after the casting process. Only at the time of 2 hours

after the end of the casting process was a mild deviation observed in the

temperature interval 684.15–744.15 K between simulation results based on

theoretical and experimental Cp. The differences can be seen at a border of

concave regions of the mould, where the more distinct warming is evident. This

feature, obtained by experimental Cp dependence, is very similar (more close) to

the results obtained by real thermo-vision measurements in comparison with the

results obtained with calculated Cp. Furthermore, a very important fact is that the



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temperature field on the ingot surface, after stripping, is identical with the

calculated temperature field using the dependence of Cp on the temperature

obtained by the DSC experiment.

It is possible to state from the obtained results that the experimental value of Cp

temperature dependence in the observed temperature interval contributed to the

results (simulations) that were more accurate and closer to the results obtained by

real thermo-vision measurements. Although the differences in Cp dependences in

the region of phase transitions significantly differ, the simulation results are very

close (in majority the same). It is possible to state that a lack of proper basic

experimental data still persists and that there are differences between the used

data. More precise data are necessary for improvement of simulations and

consequently for more precise setting of real conditions of technological processes

leading to the improvement of properties of the final product.

Conclusions

The following conclusions were formulated on the basis of the obtained

experimental results from DTA, DSC analyses and from comparison of real

thermo-vision measurements and simulations using heat capacity calculated by

the CompuTherm and experimental heat capacity measured using continuous

method and SETARAM MHTC (Multi High Temperature Calorimeter) equipped

with the 3D DSC sensor:

- The experiments must be performed very carefully with respect to the possible

massive decarburisation.

- Two running phase transitions were detected by DTA and DSC analyses in the

studied ingot mould.



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- Temperature of the Curie point was found to be 1019 K (DTA) and 1036 K

(DSC) respectively.

- The second one is the transition α + Cgrafitic→γ, which takes place between the

temperatures 1071–1108 K (DTA) and 1079–1131 K (DSC) respectively.

- The heat capacity dependence obtained by the CompuTherm shows only one

running phase transition (peak). It is not clear, to which phase transition this peak

is related to. Probably, the authors of the CompuTherm suppose that the peak

includes both: magnetic transition and transition of α + Cgrafitic → γ.

- The experimental Cp values are very close to the calculated values in the

temperature interval of 500–1000 K and in the interval of 1175–1300 K. More

distinct deviations are in the temperature interval of 1000–1175 K.

- The results of simulations of casting process using experimental and calculated

Cp values differed slightly after only 2 hours after the end of casting process. The

results obtained by experimental Cp dependence (after 2 hours) are closer to the

results obtained using thermo–vision measurements.

- The simulation results obtained using experimental Cp dependence seem to be

more precise in comparison with the calculated Cp dependence.

- Despite relatively significant differences in the Cp dependence in the phase

transition region it seems that these differences have no considerable impact on

the simulation results (it is possible to use the calculated and measured Cp

dependence also for obtaining very close–almost the same results).

Experimental measurements were performed in order to obtain our own data of

the temperature dependence of Cp on the temperature for a hematite ingot mould.

Simulations leading to description of temperature fields in the ingot mould were

performed. The obtained results showed the necessity of experimental



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measurements and consequently improvement of present databases, as well as SW

used for thermo–dynamical calculations and simulations.

Future work is planned and will be focused on the study of the origin of possible

defects and on segregation processes that are strongly dependent on the changes

of the temperature field in the ingot alone, and in the ingot mould as well.

Acknowledgements

This work was carried out within the scope of the projects of the Czech Science Foundation

No. P107/11/1566, Program Project TIP No.: FR-TI3/243 of Ministry of Industry and Trade of the

Czech Republic., the project No. CZ.1.05/2.1.00/01.0040 "Regional Materials Science and

Technology Centre" within the frame of the operation programme "Research and Development for

Innovations" financed by the Structural Funds and from the state budget of the Czech Republic

and of the grant project No. 1610/2012/G1 under the financial support of FRVŠ.

References

1 Komorová L, Imriš I. Thermodynamics in metallurgy. 1st ed. Bratislava: Alfa; 1990.

2 Žaludová M et al. Experimental study of Fe–C–O based system above 1000 °C. J Therm Anal

Calorim. 2012; doi:10.1007/s10973-012-2847-8

3 Smetana B et al. Phase transition temperatures of Sn–Zn–Al system and their comparison with

calculated phase diagrams. J Therm Anal Calorim. 2012; doi: 10.1007/s10973-012-2318-2

4 Zlá S et al. Determination of thermophysical properties of high temperature alloy IN713LC by

thermal analysis. J Therm Anal Calorim. 2012; doi: 10.1007/s10973-012-2304-8

5 Smetana B et al. Phase transformation temperatures of pure iron and low alloyed steels in the

low temperature region using DTA. Int J Mater Res. 2010; doi:10.3139/146.110283

6 Przeliorz R et al. Investigation of phase transformations in ductile cast iron of differential

scanning calorimetry. Mater Sci Eng. 2011; doi:10.1088/1757-899X/22/1/012019

7 Smetana B et al. Application of high temperature DTA to micro-alloyed steels. Metalurgija.

2012;51(1):121–4.

8 Dudek R et al. Interpretation of inorganic melts surface properties on the basis of chemical status

and structural relations. Int J Mater Res. 2008; doi:10.3139/146.101770

9 Vitásková S et al. Modelling of surface properties of oxide melts with variable basicity.

Proceedings paper, METAL 2011: 20th Anniversary International Conference on Metallurgy and

Materials, ISBN 978-80-87294-24-6, pp. 80-85.

10 Coll. of authors. TG and MHTC manual version. France: Setaram; 2009.

11 Tkadlečková et al. Testing of numerical model settings for simulation of steel ingot casting and

solidification. Proceedings paper, METAL 2011: 20th Anniversary International Conference on

Metallurgy and Materials, ISBN 978-80-87294-24-6, pp. 61–7.



15

12 Tkadlečková et al. Comparison of Numerical Results with Thermography Measurement.

Proceedings paper, METAL 2012: 21th Anniversary International Conference on Metallurgy and

Materials 2012, ISBN 978-80-87294-29-1.

13 Tkadlečková et al. Verification of thermo-dynamic parameters of numerical model of filling

and solidification of heavy forging ingot. Proceedings paper, Oceláři 2012, ISBN 978-80-87294-

28-4, pp. 76–83.

14 Tkadlečková et al. Setting of numerical simulation of filling and solidification of heavy steel

ingot based on real casting conditions. Mater Tehnol. 2012;46(4):399–402.

15 Tkadlečková et al. Verification of influence of boundary parameters of casting of steel ingots

on the size of bulk defects. Hutnické listy. 2012;65(2):3 –7.

16 Michalek K et al. Physical modelling of bath homogenisation in argon stirred ladle.

Metalurgija. 2009;48(4):215–8.

17 Janiszewski K. Influence of slenderness ratios of a multi-hole ceramic filters at the

effectiveness of process of filtration of non-metallic inclusions from liquid steel. Arch Metall

Mater. 2012; doi: 10.2478/v10172-012-0025-4

18 Witusiewicz VT et al. Enthalpy of Formation and Heat Capacity of Fe-Mn Alloys. Metall

Mater Trans B. 2003; doi: 10.1007/s11663-003-0008-y

19 Chen CS. Thermal properties modelling for freezing fruit and vegetable juices: correlation of

heat content, specific heat and ice content. Proc Fla State Hort Soc. 1984; 97:82–4.

20 Ryš P et al. Material science I, Metal science 4. 1st ed. Praha: ACADEMIA; 1975.

Figure Captions

Fig. 1 Ingot mould, A-real ingot mould, B-CAD geometry of ingot mould, C-final computational

mesh of ingot mould, D-final computational mesh of ingot

Fig. 2 Scheme of continuous Cp method, X - section of values used for Cp evaluation

Fig. 3 Comparison of TG and DTA curves obtained at 10 and 20 K min-1

Fig. 4 Comparison of apparent heat capacities calculated with use of CompuTherm and

experimentally obtained values

Fig. 5 Comparison of measured and calculated temperature fields of ingot mould

Table Captions

Table 1 Chemical composition of studied ingot mould, wt. %

Table 2 Apparent heat capacity of studied ingot mould, experimental (Exp.) and calculated (Calc.)

values



Table 1 Chemical composition of studied ingot mould, wt %

Sample C Si Mn P S Cr Hematite

mould 3.6 1.5 0.7 0.02 0.02 0.1

Table 2 Apparent heat capacity of studied ingot mould, experimental (Exp.) and calculated (Calc.) values

T/K Cp/J K-1 g-1

Exp.a Calc. ∆b 500 0.57±0.02 0.50 12.7 525 0.56±0.02 0.52 8.7 550 0.57±0.02 0.54 5.6 575 0.57±0.02 0.56 3.2 600 0.58±0.02 0.58 1.5 625 0.60±0.02 0.60 0.0 650 0.61±0.02 0.62 1.2 675 0.62±0.01 0.64 2.4 700 0.63±0.01 0.66 3.5 725 0.65±0.01 0.68 4.7 750 0.66±0.01 0.70 5.8 775 0.67±0.01 0.72 6.9 800 0.68±0.01 0.74 7.9 825 0.70±0.01 0.76 8.6 850 0.71±0.01 0.78 8.8 875 0.73±0.01 0.80 8.5 900 0.76±0.01 0.82 7.4 925 0.79±0.01 0.84 5.4 950 0.84±0.01 0.86 2.4 975 0.89±0.01 0.88 1.6

1000 0.96±0.01 0.90 6.5 1005 0.97±0.02 0.90 7.6 1010 0.99±0.01 1.13 13.9 1015 1.01±0.02 1.50 48.7 1020 1.03±0.01 1.87 82.3 1025 1.04±0.02 2.24 114.5 1030 1.06±0.02 2.21 108.2 1035 1.08±0.02 2.01 85.0 1040 1.05±0.02 1.80 70.4 1045 1.01±0.02 1.59 56.7 1050 0.98±0.02 1.38 40.8 1055 0.95±0.02 1.17 22.8 1060 0.93±0.02 0.96 3.0 1065 0.92±0.08 0.75 18.4 1070 0.91±0.14 0.72 21.7 1075 0.97±0.14 0.72 26.1 1080 1.13±0.14 0.72 36.1 1085 1.26±0.13 0.72 42.6 1090 1.37±0.13 0.72 47.1 1095 1.45±0.14 0.73 50.0 1100 1.51±0.06 0.73 51.9 1125 1.08±0.04 0.74 31.8 1150 0.85±0.02 0.75 12.4 1175 0.78±0.02 0.76 2.7 1200 0.77±0.02 0.77 0.1 1225 0.77±0.03 0.78 1.2 1250 0.76±0.04 0.79 4.1 1275 0.74±0.04 0.80 7.4 1300 0.77±0.03 0.81 4.8

aUncertainties are the standard deviations of three replicates

b∆=100(|Cp,Exp.-Cp,Calc|/Cp,Exp.)



Fig. 1 Ingot mould, A-real ingot mould, B-CAD geometry of ingot mould, C-final computational mesh of ingot

mould, D-final computational mesh of ingot

Fig. 2 Scheme of continuous Cp method, X - section of values used for Cp evaluation

Fig. 3 Comparison of TG and DTA curves obtained at 10 and 20 K min-1



Fig. 4 Comparison of apparent heat capacities calculated with use of CompuTherm and experimentally obtained

values

Fig. 5 Comparison of measured and calculated temperature fields of ingot mould



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Experimental Verification of Hematite Ingot Mould Heat - DSpace